Question

Find the distance between points A and B, located on the opposite shores of a river, if on one of the shores following segments have been drawn and measured SB=60m, SC=80m, SD=180m and BC∥AD.

Answer 1

Answer:

AB=$75m$

Step-by-step explanation:

In the $\Delta SCB$ and $\Delta SDA$

$\angle S=\angle S\\BC||AD\\\Rightarrow\angle SBC=\angle SAD\\\angle SCB =\angle SDA$

$By\ AAA\ \Delta\ and\ \Delta SDA\ are\ similar\\\\ \Rightarrow\frac{SC}{SD} =\frac{SB}{SA} \\\\ \frac{80}{180} =\frac{60}{SA}\\\\ SA=60\times\frac{180}{80} \\\\SA=135\\\\AB=SA-SB\\\\=135-60\\\\=75m$